If we evaluate at infinity, we get the following:
![\large\displaystyle\text{$\begin{gathered}\sf \displaystyle L = \lim_{x \to \infty}{\frac{7x - 1}{\sqrt[3]{5x^3 + 4x - 2}}} = \frac{\infty}{\infty} \end{gathered}$}](https://tex.z-dn.net/?f=%5Clarge%5Cdisplaystyle%5Ctext%7B%24%5Cbegin%7Bgathered%7D%5Csf%20%5Cdisplaystyle%20L%20%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%7B%5Cfrac%7B7x%20-%201%7D%7B%5Csqrt%5B3%5D%7B5x%5E3%20%2B%204x%20-%202%7D%7D%7D%20%3D%20%5Cfrac%7B%5Cinfty%7D%7B%5Cinfty%7D%20%5Cend%7Bgathered%7D%24%7D)
Which is an indeterminacy of ∞ / ∞. Therefore, we must multiply and divide by the highest degree monomial (either in numerator or denominator). In this case it is 1/x—since the denominator involves a cube root, then the "monomial" x³ is considered to be a monomial of degree 1—. So:
![\large\displaystyle\text{$\begin{gathered}\sf L= \lim_{x \to \infty}\frac{7x-1 }{\sqrt[3]{5x^3+4x-2 } }\cdot\frac{\frac{1}{x} }{\frac{1}{x} } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \ \ = \lim_{x \to \infty}\frac{\frac{7x}{x}-\frac{1}{x } }{\sqrt[3]{\frac{5x^3}{ x^{3} }+\frac{4x}{x^{3} }-\frac{2}{x^{3} } } } \end{gathered}$}\\](https://tex.z-dn.net/?f=%5Clarge%5Cdisplaystyle%5Ctext%7B%24%5Cbegin%7Bgathered%7D%5Csf%20L%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%5Cfrac%7B7x-1%20%7D%7B%5Csqrt%5B3%5D%7B5x%5E3%2B4x-2%20%7D%20%20%7D%5Ccdot%5Cfrac%7B%5Cfrac%7B1%7D%7Bx%7D%20%20%7D%7B%5Cfrac%7B1%7D%7Bx%7D%20%20%7D%20%20%20%5Cend%7Bgathered%7D%24%7D%5C%5C%5Clarge%5Cdisplaystyle%5Ctext%7B%24%5Cbegin%7Bgathered%7D%5Csf%20%5C%20%5C%20%20%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%5Cfrac%7B%5Cfrac%7B7x%7D%7Bx%7D-%5Cfrac%7B1%7D%7Bx%20%7D%20%20%20%7D%7B%5Csqrt%5B3%5D%7B%5Cfrac%7B5x%5E3%7D%7B%20x%5E%7B3%7D%20%7D%2B%5Cfrac%7B4x%7D%7Bx%5E%7B3%7D%20%20%7D-%5Cfrac%7B2%7D%7Bx%5E%7B3%7D%20%7D%20%20%20%20%7D%20%20%7D%20%20%20%20%5Cend%7Bgathered%7D%24%7D%5C%5C)
![\large\displaystyle\text{$\begin{gathered}\sf \ \ = \lim_{x \to \infty}\frac{7-\frac{1}{x} }{\sqrt[3]{ 5+\frac{4 }{x^{2} } -\frac{2}{x^{3} } } } \end{gathered}$}](https://tex.z-dn.net/?f=%5Clarge%5Cdisplaystyle%5Ctext%7B%24%5Cbegin%7Bgathered%7D%5Csf%20%5C%20%5C%20%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%5Cfrac%7B7-%5Cfrac%7B1%7D%7Bx%7D%20%20%7D%7B%5Csqrt%5B3%5D%7B%205%2B%5Cfrac%7B4%20%7D%7Bx%5E%7B2%7D%20%7D%20-%5Cfrac%7B2%7D%7Bx%5E%7B3%7D%20%7D%20%7D%20%20%7D%20%20%20%5Cend%7Bgathered%7D%24%7D)
That when "evaluating at infinity" we have:
![\large\displaystyle\text{$\begin{gathered}\sf \displaystyle L = \lim_{x \to \infty}{\frac{7 - \frac{1}{x}}{\sqrt[3]{5 + \frac{4}{x^2} - \frac{2}{x^3}}}} = \frac{7 - 0}{\sqrt[3]{5 + 0 - 0}} = \frac{7}{\sqrt[3]{5}} \end{gathered}$}](https://tex.z-dn.net/?f=%5Clarge%5Cdisplaystyle%5Ctext%7B%24%5Cbegin%7Bgathered%7D%5Csf%20%5Cdisplaystyle%20L%20%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%7B%5Cfrac%7B7%20-%20%5Cfrac%7B1%7D%7Bx%7D%7D%7B%5Csqrt%5B3%5D%7B5%20%2B%20%5Cfrac%7B4%7D%7Bx%5E2%7D%20-%20%5Cfrac%7B2%7D%7Bx%5E3%7D%7D%7D%7D%20%3D%20%5Cfrac%7B7%20-%200%7D%7B%5Csqrt%5B3%5D%7B5%20%2B%200%20-%200%7D%7D%20%3D%20%5Cfrac%7B7%7D%7B%5Csqrt%5B3%5D%7B5%7D%7D%20%5Cend%7Bgathered%7D%24%7D)
Answer:
24 minutes
Step-by-step explanation:
If each half is 45 minutes long, and Evelyn played until there were only 21 minutes left in the second half, she played for 24 minutes in the second half.
21 minutes + 24 minutes = 45 minutes
Answer:1. 152.4
2. 0.0009
3. 680
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
7x-1=4x+5
7x=4x+6
3x=6
x=2
Answer:
B is your answer
Step-by-step explanation:
<em><u>PLEASE MARK BRAINLIEST</u></em>